Statistics of the zeros of $\xi'(s)$

The Riemann $\xi$-function is real on the 1/2-line and has all of its zeros there (assuming the Riemann Hypothesis). It is an entire function of order 1; because of its functional equation, $\xi(1/2+i\sqrt{z})$ is an entire function of order 1/2. It follows that the Riemann Hypothesis implies that all zeros of $\xi'(s)$ are on the 1/2-line. (See [ MR 84g:10070] for proofs of these statements.) Assuming the Riemann Hypothesis to be true, one can ask about the vertical distribution of zeros of $\xi'(s)$, and more generally of $\xi^{(m)}(s)$. It seems that the zeros of higher derivatives will become more and more regularly spaced; can these distributions be expressed in a simple way using random matrix theory? See the unpublished paper [Differentiation evens out zero spacings] of David Farmer.

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